We present the global phase diagrams for a compressible polymer-solvent system at the mathematical double point and its environment by using the full Tompa model for varying numbers of segments in each polymer chain. A principal transition mechanism is a mathematical double point at which two critical lines meet and exchange branches. We present the critical lines in the density-density and the P, T planes in detail. The locations of all significant features of the phase diagrams are described and compared with Scott and van Konynenburg phase diagram classifications. We find the type II, type III or type IV phase diagram behaviors of the Scott and van Konynenburg classifications. It is also found that the critical lines and phase behavior are extremely sensitive to small modifications in the chain length parameter.